# Eigen-energies and eigenstates of a tri-atomic system

## Homework Statement

An extra electron is added to one atom of a tri-atomic molecule. The electron has equal probability to jump to either of the other two atoms.

(a) Find the eigen-energies for the system. Assume that the new electron energy $\bar{E_{0}}$ is close to the non-hopping case energy $E_{0}$. Draw an energy level diagram.

(b) Find one normalized eigenstate for the system.

## The Attempt at a Solution

(a) The only information available to me are that the the electron has equal probability to jump to either of the other two atoms. and the system has three atoms. How can these two pieces of information be used to find the eigen-energies of the system? Am I missing something?

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DrDu
I suppose you can assume that the three atoms are identical.

How might that help me? For now, all I can say is that the electron has the same eigen-energy for being in any of the three atoms i.e. in any one of the three states.

Is that all I can say for the eigen-energies of the system?

DrDu